Solve Easy Vector Problem: Find Displacement of Clock Hands from 3pm-6pm

  • Thread starter Thread starter whizbang21
  • Start date Start date
  • Tags Tags
    Vector
AI Thread Summary
To find the displacements of the clock hands from 3 PM to 6 PM, the minute hand, which completes a full rotation every hour, will have a displacement of zero since it returns to the same position. The hour hand, however, moves from the 3 o'clock position to the 6 o'clock position, covering an angular displacement of 90 degrees. The Cartesian coordinates for the tip of the hour hand at 3 PM are (0.23, 0) and at 6 PM are (0, 0.23). The displacement vector for the hour hand can be calculated using the difference in coordinates, resulting in a displacement of (-0.23, 0.23). Understanding the definitions of displacement and vector quantities is crucial for solving this problem accurately.
whizbang21
Messages
6
Reaction score
0
1. A wall clock has a minute hand with a length of 0.45 m and an hour hand with a length of 0.23 m. Take the center of the clock as the origin, and use a Cartesian coordinate system with the positive x-axis pointing to 3 o'clock and the positive y-axis pointing to 12 o'clock. Find the displacements of the tip of each hand (that is, ΔAarrowbolditalic and ΔBarrowbolditalic) when the time advances from 3:00 P.M. to 6:00 P.M. (Aarrowbolditalic and Barrowbolditalic represent the tip of the hour hand and the tip of the minute hand, respectively.)

Let the +y direction be straight up and the +x direction be to the right. Recall the definition of displacement, and remember that positions are vector quantities.

Homework Equations


dont know, tried Pythagorean theorem.

The Attempt at a Solution


the part dealing with the minute hand is obviously 0. but as far as the hour hand, I've tried using the pythagorean theorem to calculate the displacement which would just be sqrt((.23^2)+(.23^2)^2) but apparently that was wrong, or maybe i just put the wrong sign. only have 1 more submission so not about to guess it.
 
Physics news on Phys.org
halp
 
can you calculate their angular displacements?
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top